firework trajectories
There is plenty of science behind fireworks, much more than lighting a match to black powder. By the way; an obvious disclaimer — please don’t try that at home. While black powder (a mix of sulfur, charcoal, and a source of potassium nitrate) introduced to oxygen and a source of lighting are responsible for the basic explosion and noise, other aspects of a firework are more complex. Aspects such as height, shape, size and color of a firework are crafted with additional help from chemistry and physics with a little pinch of good luck and good weather thrown in.
For example, the way a firework is launched takes chemistry and physics into consideration. The process is very similar to the way a cannon ball is shot from its cannon.  “Lift charge” is placed between the pyrotechnic compounds and the bottom of a strong container – once the element is ignited, the lift charge propels the firework up – this is chemistry in action. Where physics comes into play is determining how high you want the firework to go in the sky. How high you want it to go is dependent only on the initial velocity of the firework – typically larger for larger fireworks.
Small firework shells, like some of the biggest you can buy for the home consumer, may reach a height in the neighborhood of 200. Big professional shows use larger artillery shells (10 times the size or more) that can reach altitudes of more than 1000 feet or more.  For the best aesthetics and safety  from falling debris for the audience, larger fireworks are shot off higher in the sky.  If everything goes right with the lift charge and other elements of the design, the firework will completely explode at or near the apex of its ascent.
There is so much more to say about the science of fireworks, these are just a few introductory ideas to get you thinking about how those fireworks you shoot off actually work.  Stay tuned for more!